Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,2,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2496.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(19.9306603445\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1248) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.622216 | −0.278263 | −0.139132 | − | 0.990274i | \(-0.544431\pi\) | ||||
−0.139132 | + | 0.990274i | \(0.544431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.42864 | 1.67387 | 0.836934 | − | 0.547304i | \(-0.184346\pi\) | ||||
0.836934 | + | 0.547304i | \(0.184346\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.80642 | −1.75070 | −0.875351 | − | 0.483487i | \(-0.839370\pi\) | ||||
−0.875351 | + | 0.483487i | \(0.839370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.622216 | 0.160655 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.42864 | 1.01600 | 0.508000 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508000 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.42864 | −0.966408 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.85728 | −1.84687 | −0.923435 | − | 0.383754i | \(-0.874631\pi\) | ||||
−0.923435 | + | 0.383754i | \(0.874631\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61285 | −0.922570 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.18421 | −1.29032 | −0.645161 | − | 0.764047i | \(-0.723210\pi\) | ||||
−0.645161 | + | 0.764047i | \(0.723210\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.80642 | 1.01077 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.75557 | −0.465776 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.755569 | −0.124215 | −0.0621074 | − | 0.998069i | \(-0.519782\pi\) | ||||
−0.0621074 | + | 0.998069i | \(0.519782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.37778 | 0.527521 | 0.263761 | − | 0.964588i | \(-0.415037\pi\) | ||||
0.263761 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.61285 | 1.16095 | 0.580474 | − | 0.814279i | \(-0.302867\pi\) | ||||
0.580474 | + | 0.814279i | \(0.302867\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.622216 | −0.0927544 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.80642 | 0.263494 | 0.131747 | − | 0.991283i | \(-0.457941\pi\) | ||||
0.131747 | + | 0.991283i | \(0.457941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.6128 | 1.80184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.75557 | −0.653228 | −0.326614 | − | 0.945158i | \(-0.605908\pi\) | ||||
−0.326614 | + | 0.945158i | \(0.605908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.61285 | 0.487156 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.42864 | −0.586588 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0509 | −1.43870 | −0.719349 | − | 0.694648i | \(-0.755560\pi\) | ||||
−0.719349 | + | 0.694648i | \(0.755560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.10171 | 1.03732 | 0.518659 | − | 0.854981i | \(-0.326431\pi\) | ||||
0.518659 | + | 0.854981i | \(0.326431\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.42864 | 0.557956 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.622216 | 0.0771764 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.04149 | −0.982424 | −0.491212 | − | 0.871040i | \(-0.663446\pi\) | ||||
−0.491212 | + | 0.871040i | \(0.663446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.85728 | 1.06629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.05086 | −0.836783 | −0.418391 | − | 0.908267i | \(-0.637406\pi\) | ||||
−0.418391 | + | 0.908267i | \(0.637406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.24443 | 0.847897 | 0.423948 | − | 0.905686i | \(-0.360644\pi\) | ||||
0.423948 | + | 0.905686i | \(0.360644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.61285 | 0.532646 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.7146 | −2.93045 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.05086 | 0.334875 | 0.167437 | − | 0.985883i | \(-0.446451\pi\) | ||||
0.167437 | + | 0.985883i | \(0.446451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.24443 | −0.134978 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.86665 | −0.197864 | −0.0989321 | − | 0.995094i | \(-0.531543\pi\) | ||||
−0.0989321 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.42864 | −0.464248 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.18421 | 0.744968 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.75557 | −0.282715 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.755569 | −0.0767164 | −0.0383582 | − | 0.999264i | \(-0.512213\pi\) | ||||
−0.0383582 | + | 0.999264i | \(0.512213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.80642 | −0.583568 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7146 | 1.56366 | 0.781828 | − | 0.623494i | \(-0.214287\pi\) | ||||
0.781828 | + | 0.623494i | \(0.214287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.1017 | −1.78361 | −0.891807 | − | 0.452416i | \(-0.850562\pi\) | ||||
−0.891807 | + | 0.452416i | \(0.850562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.75557 | 0.268916 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3461 | −1.48357 | −0.741784 | − | 0.670639i | \(-0.766020\pi\) | ||||
−0.741784 | + | 0.670639i | \(0.766020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.7146 | −1.50518 | −0.752591 | − | 0.658488i | \(-0.771196\pi\) | ||||
−0.752591 | + | 0.658488i | \(0.771196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.755569 | 0.0717154 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4701 | 1.36124 | 0.680618 | − | 0.732639i | \(-0.261712\pi\) | ||||
0.680618 | + | 0.732639i | \(0.261712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.51114 | 0.513916 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.85728 | 0.811945 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.7146 | 2.06496 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.37778 | −0.304565 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.98126 | 0.534981 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.8573 | −1.85078 | −0.925392 | − | 0.379011i | \(-0.876264\pi\) | ||||
−0.925392 | + | 0.379011i | \(0.876264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.61285 | −0.670274 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3684 | 0.905893 | 0.452946 | − | 0.891538i | \(-0.350373\pi\) | ||||
0.452946 | + | 0.891538i | \(0.350373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.6128 | 1.70065 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.622216 | 0.0535518 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8479 | −1.69572 | −0.847861 | − | 0.530219i | \(-0.822110\pi\) | ||||
−0.847861 | + | 0.530219i | \(0.822110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.75557 | −0.573000 | −0.286500 | − | 0.958080i | \(-0.592492\pi\) | ||||
−0.286500 | + | 0.958080i | \(0.592492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.80642 | −0.152128 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.80642 | 0.485558 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.24443 | 0.103344 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.6128 | −1.04029 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.13335 | 0.174771 | 0.0873855 | − | 0.996175i | \(-0.472149\pi\) | ||||
0.0873855 | + | 0.996175i | \(0.472149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.67307 | 0.136153 | 0.0680763 | − | 0.997680i | \(-0.478314\pi\) | ||||
0.0680763 | + | 0.997680i | \(0.478314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.47013 | 0.359049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.1240 | −1.20703 | −0.603513 | − | 0.797353i | \(-0.706233\pi\) | ||||
−0.603513 | + | 0.797353i | \(0.706233\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.75557 | 0.377141 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −39.2257 | −3.09142 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7748 | 1.23558 | 0.617788 | − | 0.786345i | \(-0.288029\pi\) | ||||
0.617788 | + | 0.786345i | \(0.288029\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.61285 | −0.281260 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.31756 | 0.566250 | 0.283125 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283125 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.42864 | 0.338667 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.51114 | −0.571061 | −0.285531 | − | 0.958370i | \(-0.592170\pi\) | ||||
−0.285531 | + | 0.958370i | \(0.592170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.4286 | −1.54426 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0509 | 0.830633 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.7556 | −1.10288 | −0.551441 | − | 0.834214i | \(-0.685922\pi\) | ||||
−0.551441 | + | 0.834214i | \(0.685922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.10171 | −0.304878 | −0.152439 | − | 0.988313i | \(-0.548713\pi\) | ||||
−0.152439 | + | 0.988313i | \(0.548713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.10171 | −0.598896 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.470127 | 0.0345644 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6128 | −0.849216 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.42864 | −0.322136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.266706 | −0.0192982 | −0.00964909 | − | 0.999953i | \(-0.503071\pi\) | ||||
−0.00964909 | + | 0.999953i | \(0.503071\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.2034 | −1.88616 | −0.943082 | − | 0.332561i | \(-0.892087\pi\) | ||||
−0.943082 | + | 0.332561i | \(0.892087\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.622216 | −0.0445578 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.8479 | −1.12912 | −0.564558 | − | 0.825393i | \(-0.690954\pi\) | ||||
−0.564558 | + | 0.825393i | \(0.690954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3684 | 0.734998 | 0.367499 | − | 0.930024i | \(-0.380214\pi\) | ||||
0.367499 | + | 0.930024i | \(0.380214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.04149 | 0.567203 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.85728 | −0.621659 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.10171 | −0.146790 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.85728 | −0.615623 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.7146 | −1.77871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.05086 | 0.483117 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.73683 | −0.323049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.8163 | −2.15983 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.24443 | −0.489533 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | −0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.69535 | −0.314424 | −0.157212 | − | 0.987565i | \(-0.550251\pi\) | ||||
−0.157212 | + | 0.987565i | \(0.550251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.61285 | −0.307523 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.80642 | 0.385386 | 0.192693 | − | 0.981259i | \(-0.438278\pi\) | ||||
0.192693 | + | 0.981259i | \(0.438278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.7146 | 1.69189 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.24443 | 0.474598 | 0.237299 | − | 0.971437i | \(-0.423738\pi\) | ||||
0.237299 | + | 0.971437i | \(0.423738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.12399 | −0.0733207 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0000 | 0.779484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6637 | 0.689778 | 0.344889 | − | 0.938644i | \(-0.387917\pi\) | ||||
0.344889 | + | 0.938644i | \(0.387917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.73329 | −0.369314 | −0.184657 | − | 0.982803i | \(-0.559117\pi\) | ||||
−0.184657 | + | 0.982803i | \(0.559117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.84791 | −0.501385 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.42864 | −0.281788 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.05086 | −0.193340 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.6128 | −1.49043 | −0.745215 | − | 0.666824i | \(-0.767653\pi\) | ||||
−0.745215 | + | 0.666824i | \(0.767653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 51.4291 | 3.23332 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.24443 | 0.0779293 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2444 | −0.701408 | −0.350704 | − | 0.936486i | \(-0.614058\pi\) | ||||
−0.350704 | + | 0.936486i | \(0.614058\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.34614 | −0.207919 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.38715 | 0.270523 | 0.135262 | − | 0.990810i | \(-0.456812\pi\) | ||||
0.135262 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.95899 | 0.181769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.86665 | 0.114237 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.51114 | −0.457962 | −0.228981 | − | 0.973431i | \(-0.573539\pi\) | ||||
−0.228981 | + | 0.973431i | \(0.573539\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.06022 | −0.368132 | −0.184066 | − | 0.982914i | \(-0.558926\pi\) | ||||
−0.184066 | + | 0.982914i | \(0.558926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.42864 | 0.268033 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.7841 | 1.61514 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.488863 | −0.0293729 | −0.0146865 | − | 0.999892i | \(-0.504675\pi\) | ||||
−0.0146865 | + | 0.999892i | \(0.504675\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.18421 | −0.430107 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0923 | 0.781024 | 0.390512 | − | 0.920598i | \(-0.372298\pi\) | ||||
0.390512 | + | 0.920598i | \(0.372298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3461 | −1.38778 | −0.693892 | − | 0.720079i | \(-0.744106\pi\) | ||||
−0.693892 | + | 0.720079i | \(0.744106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.75557 | 0.163226 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.9590 | 0.883001 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.755569 | 0.0442922 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.0923 | −0.764863 | −0.382431 | − | 0.923984i | \(-0.624913\pi\) | ||||
−0.382431 | + | 0.923984i | \(0.624913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.87601 | 0.400337 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.80642 | 0.336923 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.85728 | 0.512230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.7146 | 1.94327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.7146 | −0.902778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.04101 | −0.288647 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.0415 | 1.82870 | 0.914352 | − | 0.404920i | \(-0.132701\pi\) | ||||
0.914352 | + | 0.404920i | \(0.132701\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.1017 | 1.02977 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0830 | 1.36562 | 0.682810 | − | 0.730596i | \(-0.260758\pi\) | ||||
0.682810 | + | 0.730596i | \(0.260758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.7146 | 1.56652 | 0.783260 | − | 0.621695i | \(-0.213556\pi\) | ||||
0.783260 | + | 0.621695i | \(0.213556\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.75557 | −0.155259 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.0923 | 0.960002 | 0.480001 | − | 0.877268i | \(-0.340636\pi\) | ||||
0.480001 | + | 0.877268i | \(0.340636\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.6128 | 0.650195 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3461 | 0.856538 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.85728 | 0.492832 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.61285 | 0.255875 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.7146 | 0.869017 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.18421 | 0.394880 | 0.197440 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197440 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.755569 | −0.0414049 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.00354 | 0.273373 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.285442 | 0.0155490 | 0.00777451 | − | 0.999970i | \(-0.497525\pi\) | ||||
0.00777451 | + | 0.999970i | \(0.497525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.4701 | −0.785909 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.7146 | 2.25897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.8573 | 1.34217 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.51114 | −0.296710 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.2034 | 1.29931 | 0.649654 | − | 0.760230i | \(-0.274914\pi\) | ||||
0.649654 | + | 0.760230i | \(0.274914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7556 | 0.682790 | 0.341395 | − | 0.939920i | \(-0.389101\pi\) | ||||
0.341395 | + | 0.939920i | \(0.389101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0923 | 1.12263 | 0.561316 | − | 0.827602i | \(-0.310295\pi\) | ||||
0.561316 | + | 0.827602i | \(0.310295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.38715 | 0.232846 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.85728 | −0.468777 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.1338 | −0.798733 | −0.399366 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399366 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.612848 | 0.0322551 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.7146 | −1.19221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.50760 | −0.235938 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.9590 | −0.989651 | −0.494826 | − | 0.868992i | \(-0.664768\pi\) | ||||
−0.494826 | + | 0.868992i | \(0.664768\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.37778 | 0.175840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.0607 | −1.09342 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.97773 | −0.154181 | −0.0770904 | − | 0.997024i | \(-0.524563\pi\) | ||||
−0.0770904 | + | 0.997024i | \(0.524563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.98126 | −0.308871 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1432 | 0.726487 | 0.363244 | − | 0.931694i | \(-0.381669\pi\) | ||||
0.363244 | + | 0.931694i | \(0.381669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.8573 | 1.06855 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.8064 | −1.31865 | −0.659323 | − | 0.751860i | \(-0.729157\pi\) | ||||
−0.659323 | + | 0.751860i | \(0.729157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.61285 | 0.386983 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.9590 | 0.657047 | 0.328523 | − | 0.944496i | \(-0.393449\pi\) | ||||
0.328523 | + | 0.944496i | \(0.393449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.7146 | −0.895864 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.3684 | −0.523017 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.46659 | 0.375685 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.24443 | −0.162833 | −0.0814167 | − | 0.996680i | \(-0.525944\pi\) | ||||
−0.0814167 | + | 0.996680i | \(0.525944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.6128 | −0.981870 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.6035 | −1.52826 | −0.764132 | − | 0.645059i | \(-0.776833\pi\) | ||||
−0.764132 | + | 0.645059i | \(0.776833\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.18421 | 0.357871 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.622216 | −0.0309181 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.38715 | 0.217463 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.75557 | −0.432935 | −0.216468 | − | 0.976290i | \(-0.569454\pi\) | ||||
−0.216468 | + | 0.976290i | \(0.569454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.8479 | 0.979025 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −48.9403 | −2.40819 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.89829 | −0.0931834 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.75557 | 0.330822 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.8796 | 1.16659 | 0.583296 | − | 0.812259i | \(-0.301763\pi\) | ||||
0.583296 | + | 0.812259i | \(0.301763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.28544 | 0.403808 | 0.201904 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201904 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.80642 | 0.0878313 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.22570 | −0.447512 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.8796 | 1.73633 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.80642 | −0.280337 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0098 | −0.674830 | −0.337415 | − | 0.941356i | \(-0.609553\pi\) | ||||
−0.337415 | + | 0.941356i | \(0.609553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.1240 | 1.30350 | 0.651748 | − | 0.758436i | \(-0.274036\pi\) | ||||
0.651748 | + | 0.758436i | \(0.274036\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.24443 | −0.0596659 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −39.2257 | −1.87642 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.59057 | 0.219096 | 0.109548 | − | 0.993982i | \(-0.465060\pi\) | ||||
0.109548 | + | 0.993982i | \(0.465060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6128 | 0.600612 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3684 | 0.492618 | 0.246309 | − | 0.969191i | \(-0.420782\pi\) | ||||
0.246309 | + | 0.969191i | \(0.420782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.16146 | 0.0550583 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.13335 | −0.100904 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3368 | 0.487823 | 0.243911 | − | 0.969798i | \(-0.421569\pi\) | ||||
0.243911 | + | 0.969798i | \(0.421569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.6128 | −0.923533 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.67307 | −0.0786077 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.75557 | 0.129183 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.52987 | 0.258677 | 0.129338 | − | 0.991601i | \(-0.458715\pi\) | ||||
0.129338 | + | 0.991601i | \(0.458715\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8666 | 0.832133 | 0.416066 | − | 0.909334i | \(-0.363408\pi\) | ||||
0.416066 | + | 0.909334i | \(0.363408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.6766 | 1.79745 | 0.898727 | − | 0.438508i | \(-0.144493\pi\) | ||||
0.898727 | + | 0.438508i | \(0.144493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.47013 | −0.207297 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1017 | −0.467451 | −0.233726 | − | 0.972303i | \(-0.575092\pi\) | ||||
−0.233726 | + | 0.972303i | \(0.575092\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.6128 | −1.64445 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.1240 | 0.696876 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.2034 | −2.03248 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.4286 | −0.937330 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.75557 | −0.217743 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.8671 | −1.41035 | −0.705177 | − | 0.709031i | \(-0.749133\pi\) | ||||
−0.705177 | + | 0.709031i | \(0.749133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.755569 | 0.0344510 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 39.2257 | 1.78483 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.470127 | 0.0213474 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7560 | 1.16712 | 0.583559 | − | 0.812071i | \(-0.301660\pi\) | ||||
0.583559 | + | 0.812071i | \(0.301660\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.7748 | −0.713360 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.8163 | −1.25533 | −0.627665 | − | 0.778483i | \(-0.715989\pi\) | ||||
−0.627665 | + | 0.778483i | \(0.715989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.61285 | 0.162385 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.2257 | −1.40066 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.815792 | −0.0365199 | −0.0182599 | − | 0.999833i | \(-0.505813\pi\) | ||||
−0.0182599 | + | 0.999833i | \(0.505813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.31756 | −0.326925 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.8385 | 1.19667 | 0.598336 | − | 0.801245i | \(-0.295829\pi\) | ||||
0.598336 | + | 0.801245i | \(0.295829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.77784 | −0.435108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.60348 | 0.292694 | 0.146347 | − | 0.989233i | \(-0.453248\pi\) | ||||
0.146347 | + | 0.989233i | \(0.453248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.0830 | 1.41927 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.42864 | −0.195529 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.2632 | 0.496314 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4889 | −0.461300 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.51114 | 0.329702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.9813 | 1.57637 | 0.788184 | − | 0.615440i | \(-0.211022\pi\) | ||||
0.788184 | + | 0.615440i | \(0.211022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.9590 | 1.52865 | 0.764325 | − | 0.644831i | \(-0.223072\pi\) | ||||
0.764325 | + | 0.644831i | \(0.223072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.4286 | 0.891579 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.3684 | −0.625898 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.4514 | 2.41093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0509 | −0.479566 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.37778 | −0.146308 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.54861 | 0.412822 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7556 | 0.636750 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −73.2355 | −3.15448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5111 | −0.838849 | −0.419425 | − | 0.907790i | \(-0.637768\pi\) | ||||
−0.419425 | + | 0.907790i | \(0.637768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.10171 | 0.176021 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.77784 | 0.418837 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.26671 | 0.182431 | 0.0912156 | − | 0.995831i | \(-0.470925\pi\) | ||||
0.0912156 | + | 0.995831i | \(0.470925\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.10171 | 0.345773 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.85728 | −0.377333 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.1437 | −2.25990 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.470127 | −0.0199558 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.86665 | −0.248578 | −0.124289 | − | 0.992246i | \(-0.539665\pi\) | ||||
−0.124289 | + | 0.992246i | \(0.539665\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.61285 | −0.321989 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.6128 | 0.490295 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.4924 | 1.15867 | 0.579333 | − | 0.815091i | \(-0.303313\pi\) | ||||
0.579333 | + | 0.815091i | \(0.303313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00354 | −0.378782 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.42864 | 0.185985 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.4924 | −0.565631 | −0.282815 | − | 0.959174i | \(-0.591268\pi\) | ||||
−0.282815 | + | 0.959174i | \(0.591268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8796 | −0.999328 | −0.499664 | − | 0.866219i | \(-0.666543\pi\) | ||||
−0.499664 | + | 0.866219i | \(0.666543\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.266706 | 0.0111418 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.8573 | 1.70387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4514 | 1.35097 | 0.675485 | − | 0.737374i | \(-0.263935\pi\) | ||||
0.675485 | + | 0.737374i | \(0.263935\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.2034 | 1.08898 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5111 | 0.560536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.6128 | 1.14361 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.622216 | 0.0257255 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3363 | 0.715546 | 0.357773 | − | 0.933809i | \(-0.383536\pi\) | ||||
0.357773 | + | 0.933809i | \(0.383536\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.8163 | −1.31097 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8479 | 0.651896 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.8069 | −0.772307 | −0.386153 | − | 0.922435i | \(-0.626196\pi\) | ||||
−0.386153 | + | 0.922435i | \(0.626196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.51114 | −0.225935 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.3684 | −0.424351 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.8163 | 1.29998 | 0.649989 | − | 0.759944i | \(-0.274774\pi\) | ||||
0.649989 | + | 0.759944i | \(0.274774\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.28544 | −0.174807 | −0.0874034 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874034 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.04149 | −0.327475 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.1334 | −0.574603 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2444 | 0.699930 | 0.349965 | − | 0.936763i | \(-0.386193\pi\) | ||||
0.349965 | + | 0.936763i | \(0.386193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.85728 | 0.358915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.80642 | −0.0730801 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9813 | −0.968594 | −0.484297 | − | 0.874904i | \(-0.660925\pi\) | ||||
−0.484297 | + | 0.874904i | \(0.660925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.10171 | 0.0847491 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.40006 | 0.257657 | 0.128828 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128828 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.04149 | 0.323215 | 0.161607 | − | 0.986855i | \(-0.448332\pi\) | ||||
0.161607 | + | 0.986855i | \(0.448332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.85728 | 0.355430 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.26671 | −0.331199 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3426 | 0.773704 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.7146 | 1.02694 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.51114 | −0.0602530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1842 | 0.922949 | 0.461474 | − | 0.887154i | \(-0.347321\pi\) | ||||
0.461474 | + | 0.887154i | \(0.347321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9777 | 0.515005 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.6128 | −0.499739 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.05086 | −0.278928 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.51114 | −0.138682 | −0.0693408 | − | 0.997593i | \(-0.522090\pi\) | ||||
−0.0693408 | + | 0.997593i | \(0.522090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.7560 | −1.96219 | −0.981093 | − | 0.193535i | \(-0.938005\pi\) | ||||
−0.981093 | + | 0.193535i | \(0.938005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.73683 | 0.186513 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.9403 | −0.980503 | −0.490251 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490251 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 64.1659 | 2.51873 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 31.8163 | 1.24698 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7146 | −0.458426 | −0.229213 | − | 0.973376i | \(-0.573615\pi\) | ||||
−0.229213 | + | 0.973376i | \(0.573615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.45139 | −0.252077 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.24443 | 0.282632 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.51114 | 0.0588656 | 0.0294328 | − | 0.999567i | \(-0.490630\pi\) | ||||
0.0294328 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.1847 | 0.940675 | 0.470338 | − | 0.882487i | \(-0.344132\pi\) | ||||
0.470338 | + | 0.882487i | \(0.344132\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.00000 | 0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.2034 | −0.473228 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.7146 | 0.685910 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.69535 | 0.181533 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.0420 | −1.81603 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.83854 | −0.340701 | −0.170350 | − | 0.985384i | \(-0.554490\pi\) | ||||
−0.170350 | + | 0.985384i | \(0.554490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.61285 | 0.177549 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.2444 | −1.50829 | −0.754143 | − | 0.656710i | \(-0.771947\pi\) | ||||
−0.754143 | + | 0.656710i | \(0.771947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.34614 | −0.128413 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.80642 | −0.222503 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.1561 | 1.15389 | 0.576946 | − | 0.816783i | \(-0.304244\pi\) | ||||
0.576946 | + | 0.816783i | \(0.304244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.3497 | 0.471857 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.75557 | 0.181173 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5526 | −0.819900 | −0.409950 | − | 0.912108i | \(-0.634454\pi\) | ||||
−0.409950 | + | 0.912108i | \(0.634454\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.7146 | −0.976815 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.20342 | 0.159445 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.75557 | 0.255885 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.24443 | −0.274010 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.755569 | 0.0285374 | 0.0142687 | − | 0.999898i | \(-0.495458\pi\) | ||||
0.0142687 | + | 0.999898i | \(0.495458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.34614 | −0.126202 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.12399 | 0.0423317 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 69.5941 | 2.61736 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.22570 | 0.0460320 | 0.0230160 | − | 0.999735i | \(-0.492673\pi\) | ||||
0.0230160 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | −0.450035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 63.6325 | 2.38306 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.61285 | −0.135113 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.6637 | −0.398243 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3461 | 0.423140 | 0.211570 | − | 0.977363i | \(-0.432142\pi\) | ||||
0.211570 | + | 0.977363i | \(0.432142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80.1659 | −2.98554 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.73329 | 0.213223 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.22570 | 0.342634 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.0607 | −1.81956 | −0.909780 | − | 0.415090i | \(-0.863750\pi\) | ||||
−0.909780 | + | 0.415090i | \(0.863750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.2257 | 0.563143 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 53.4291 | 1.97345 | 0.986725 | − | 0.162402i | \(-0.0519241\pi\) | ||||
0.986725 | + | 0.162402i | \(0.0519241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.84791 | 0.289475 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46.6923 | 1.71993 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.0192 | 0.773204 | 0.386602 | − | 0.922247i | \(-0.373649\pi\) | ||||
0.386602 | + | 0.922247i | \(0.373649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.42864 | 0.162690 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.56199 | −0.167363 | −0.0836816 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836816 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.32741 | −0.0486324 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.05086 | 0.111625 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −67.9625 | −2.48330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.8983 | −0.799080 | −0.399540 | − | 0.916716i | \(-0.630830\pi\) | ||||
−0.399540 | + | 0.916716i | \(0.630830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.6128 | 0.860500 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.04101 | −0.0378863 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.8385 | 1.33892 | 0.669460 | − | 0.742848i | \(-0.266526\pi\) | ||||
0.669460 | + | 0.742848i | \(0.266526\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −51.4291 | −1.86676 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.8069 | 1.40675 | 0.703375 | − | 0.710819i | \(-0.251676\pi\) | ||||
0.703375 | + | 0.710819i | \(0.251676\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −69.5941 | −2.51948 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.24443 | −0.0449925 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0509 | 0.399023 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6923 | 0.890426 | 0.445213 | − | 0.895425i | \(-0.353128\pi\) | ||||
0.445213 | + | 0.895425i | \(0.353128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2444 | 0.404958 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.58120 | −0.272677 | −0.136338 | − | 0.990662i | \(-0.543533\pi\) | ||||
−0.136338 | + | 0.990662i | \(0.543533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.1397 | 1.19041 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.34614 | 0.120042 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.9590 | 0.535961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.9403 | 1.46496 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.41038 | 0.335871 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0192 | 0.464085 | 0.232042 | − | 0.972706i | \(-0.425459\pi\) | ||||
0.232042 | + | 0.972706i | \(0.425459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.38715 | −0.156187 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 64.0830 | 2.27853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.10171 | −0.287700 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.95899 | −0.104945 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.2444 | −0.823360 | −0.411680 | − | 0.911328i | \(-0.635058\pi\) | ||||
−0.411680 | + | 0.911328i | \(0.635058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.61285 | 0.127813 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.86665 | −0.0659547 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.0642 | −1.48441 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.4068 | 0.860228 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.51114 | 0.264405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.9590 | −1.29941 | −0.649704 | − | 0.760187i | \(-0.725107\pi\) | ||||
−0.649704 | + | 0.760187i | \(0.725107\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.54909 | −0.300199 | −0.150099 | − | 0.988671i | \(-0.547959\pi\) | ||||
−0.150099 | + | 0.988671i | \(0.547959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.06022 | 0.212541 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.81532 | −0.343816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.7146 | 1.17952 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.42864 | −0.154749 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.07007 | −0.0722459 | −0.0361229 | − | 0.999347i | \(-0.511501\pi\) | ||||
−0.0361229 | + | 0.999347i | \(0.511501\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.5531 | −1.41359 | −0.706796 | − | 0.707417i | \(-0.749860\pi\) | ||||
−0.706796 | + | 0.707417i | \(0.749860\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.7841 | −0.932504 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.4987 | −1.26918 | −0.634592 | − | 0.772847i | \(-0.718832\pi\) | ||||
−0.634592 | + | 0.772847i | \(0.718832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.8385 | −1.41838 | −0.709191 | − | 0.705017i | \(-0.750939\pi\) | ||||
−0.709191 | + | 0.705017i | \(0.750939\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.488863 | 0.0169585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.2257 | 0.874019 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.55310 | −0.157567 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.18421 | 0.248323 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.72345 | −0.0595001 | −0.0297500 | − | 0.999557i | \(-0.509471\pi\) | ||||
−0.0297500 | + | 0.999557i | \(0.509471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.0923 | −0.450924 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.622216 | −0.0214049 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 100.595 | 3.45647 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.3461 | 0.801238 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.69228 | 0.229409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.4924 | −1.00980 | −0.504900 | − | 0.863178i | \(-0.668471\pi\) | ||||
−0.504900 | + | 0.863178i | \(0.668471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.75557 | −0.0942385 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.01874 | 0.273915 | 0.136957 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136957 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.4291 | −1.89122 | −0.945609 | − | 0.325307i | \(-0.894532\pi\) | ||||
−0.945609 | + | 0.325307i | \(0.894532\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9590 | −0.509801 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.6227 | 0.872207 | 0.436103 | − | 0.899897i | \(-0.356358\pi\) | ||||
0.436103 | + | 0.899897i | \(0.356358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.67355 | 0.158905 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.6771 | 2.36363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.04149 | 0.272475 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.755569 | −0.0255721 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.4889 | 0.895487 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.1847 | −0.951729 | −0.475865 | − | 0.879519i | \(-0.657865\pi\) | ||||
−0.475865 | + | 0.879519i | \(0.657865\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0923 | 0.441594 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.52987 | −0.321070 | −0.160535 | − | 0.987030i | \(-0.551322\pi\) | ||||
−0.160535 | + | 0.987030i | \(0.551322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.8350 | −0.600196 | −0.300098 | − | 0.953908i | \(-0.597019\pi\) | ||||
−0.300098 | + | 0.953908i | \(0.597019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.87601 | −0.231135 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.73329 | 0.259659 | 0.129829 | − | 0.991536i | \(-0.458557\pi\) | ||||
0.129829 | + | 0.991536i | \(0.458557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −92.3694 | −3.09797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.80642 | −0.194523 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.18115 | 0.306892 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.85728 | −0.295736 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.3684 | 0.479214 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.51114 | −0.316862 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.7146 | −1.12195 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.55215 | 0.0848363 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.0830 | 1.19812 | 0.599058 | − | 0.800706i | \(-0.295542\pi\) | ||||
0.599058 | + | 0.800706i | \(0.295542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.7146 | 0.521219 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.9215 | −1.95216 | −0.976078 | − | 0.217418i | \(-0.930236\pi\) | ||||
−0.976078 | + | 0.217418i | \(0.930236\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.7146 | −0.586266 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.04101 | 0.166651 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.9180 | 1.51635 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5334 | 0.413439 | 0.206720 | − | 0.978400i | \(-0.433721\pi\) | ||||
0.206720 | + | 0.978400i | \(0.433721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.0415 | −1.05580 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.05086 | 0.232082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.48532 | 0.114597 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.1017 | −0.594538 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.0291 | −1.47736 | −0.738678 | − | 0.674059i | \(-0.764549\pi\) | ||||
−0.738678 | + | 0.674059i | \(0.764549\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 55.8578 | 1.83066 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0830 | −0.788441 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.22570 | 0.236306 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.876015 | 0.0286182 | 0.0143091 | − | 0.999898i | \(-0.495445\pi\) | ||||
0.0143091 | + | 0.999898i | \(0.495445\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.7146 | −0.904430 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.888922 | −0.0289780 | −0.0144890 | − | 0.999895i | \(-0.504612\pi\) | ||||
−0.0144890 | + | 0.999895i | \(0.504612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.9180 | −0.974263 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.75557 | 0.0896387 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.9911 | −1.42952 | −0.714759 | − | 0.699370i | \(-0.753464\pi\) | ||||
−0.714759 | + | 0.699370i | \(0.753464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.24443 | −0.235164 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0923 | −0.554257 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.4701 | −0.598306 | −0.299153 | − | 0.954205i | \(-0.596704\pi\) | ||||
−0.299153 | + | 0.954205i | \(0.596704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.165949 | 0.00536998 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.6128 | −0.375390 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −87.8992 | −2.83841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.6128 | 0.664931 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.3461 | −0.494522 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.3042 | 0.524850 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.2895 | 1.61720 | 0.808600 | − | 0.588359i | \(-0.200226\pi\) | ||||
0.808600 | + | 0.588359i | \(0.200226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.85728 | −0.284537 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.2257 | 1.13045 | 0.565223 | − | 0.824938i | \(-0.308790\pi\) | ||||
0.565223 | + | 0.824938i | \(0.308790\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.9180 | −0.959126 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.61285 | −0.147729 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58.8069 | −1.88140 | −0.940700 | − | 0.339240i | \(-0.889830\pi\) | ||||
−0.940700 | + | 0.339240i | \(0.889830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.8385 | 0.346401 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.7146 | −0.501727 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.2168 | 1.50598 | 0.752991 | − | 0.658031i | \(-0.228610\pi\) | ||||
0.752991 | + | 0.658031i | \(0.228610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.86082 | 0.314192 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | −0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.4291 | −2.14412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.4924 | −1.12745 | −0.563727 | − | 0.825961i | \(-0.690633\pi\) | ||||
−0.563727 | + | 0.825961i | \(0.690633\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.18421 | −0.227984 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.45139 | −0.204523 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.4291 | −1.56544 | −0.782718 | − | 0.622377i | \(-0.786167\pi\) | ||||
−0.782718 | + | 0.622377i | \(0.786167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.755569 | 0.0239051 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2496.2.a.bk.1.2 | 3 | ||
3.2 | odd | 2 | 7488.2.a.cy.1.2 | 3 | |||
4.3 | odd | 2 | 2496.2.a.bl.1.2 | 3 | |||
8.3 | odd | 2 | 1248.2.a.o.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 1248.2.a.p.1.2 | yes | 3 | ||
12.11 | even | 2 | 7488.2.a.cx.1.2 | 3 | |||
24.5 | odd | 2 | 3744.2.a.z.1.2 | 3 | |||
24.11 | even | 2 | 3744.2.a.ba.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.2.a.o.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
1248.2.a.p.1.2 | yes | 3 | 8.5 | even | 2 | ||
2496.2.a.bk.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2496.2.a.bl.1.2 | 3 | 4.3 | odd | 2 | |||
3744.2.a.z.1.2 | 3 | 24.5 | odd | 2 | |||
3744.2.a.ba.1.2 | 3 | 24.11 | even | 2 | |||
7488.2.a.cx.1.2 | 3 | 12.11 | even | 2 | |||
7488.2.a.cy.1.2 | 3 | 3.2 | odd | 2 |